A pinboard by
Tyler Rhodes

Graduate Student Researcher, University of California, Los Angeles


Using computers, I simulate liquid metal flowing in a magnetic field to help design fusion reactors

Fusion power generation is a popular choice for humanity’s ultimate power source because fusion is clean, safe, and sustainable. Fusion power reactors create heat by fusing hydrogen plasma at extremely high temperature and pressure. Such hot plasma would destroy the reactor’s walls except that the plasma is suspended inside the core of the reactor vessel by a very strong magnetic field. In some reactor designs, liquid metal lead-lithium (PbLi) is circulated to carry heat away from the reactor. The heat is then used for electrical power generation. Liquid metal PbLi is advantageous over other fluids because PbLi reacts favorably with neutrons from the fusion reaction; lead is a neutron multiplier and lithium reacts with neutrons to produce fuel for the reactor, tritium. However, because PbLi both flows inside the reactor's strong magnetic field and is a conductor of electricity, electromagnetic force acts on the liquid metal. Thus, the flow is governed by Maxwell's equations in addition to the usual conservation equations for mass and momentum. Such a flow is said to be a magnetohydrodynamic (MHD) flow. Using powerful computers, researchers simulate MHD flows to characterize the behavior of liquid metals flowing in conditions relevant to fusion power reactors. By uncovering the physics of MHD duct flows, researchers hope to inform fusion reactor designers and help bring the dream of fusion power to reality.


MHD flow in an insulating rectangular duct under a non-uniform magnetic field

Abstract: Followed by a review of previous studies of magnetohydrodynamic (MHD) duct flows in a non-uniform magnetic field at the entry into a magnet (fringing magnetic field), the associated MHD problem is revisited for a particular case of a nonconducting rectangular duct of a small aspect ratio ε = b/a (here, b is the duct half-width in the magnetic field direction, and a is the half-height). The suggested model includes a realistic three-component div- and curl-free fringing magnetic field as well as inertia terms and takes into account the mechanism of electric current exchange between the core of the flow and the Hartmann layers. The original three-dimensional flow equations are reduced to a quasi-two-dimensional (Q2D) form for three basic scalar quantities: the vorticity, the streamfunction and the electric potential. This Q2 D formulation implies that the velocity field in the core region between the two Hartmann layers does not change in the magnetic field direction and thus is two-dimensional, while the induced electric current forms both cross-sectional and axial circuits and is essentially three-dimensional. A new parameter R = ε2Re/Ha has been identified to characterize the role of inertia in duct flows with insulating walls (Re and Ha stand for the Reynolds and Hartmann numbers). Computations and analytical studies are performed for inertialess (R ≪ 1) and inertial (R ≫ 1) flows at ε = 0.2 for Re up to 300,000 resulting in new scaling laws for typical lengths, velocities, electric current densities and pressure drops, which provide a new theoretical basis for potential applications.PACS Codes: 47.65.-d, 47, 47.11.-j

Pub.: 01 Oct '10, Pinned: 28 Jun '17

An induction-based magnetohydrodynamic 3D code for finite magnetic Reynolds number liquid-metal flows in fusion blankets

Abstract: Most numerical analysis performed in the past for MHD flows in liquid-metal blankets were based on the assumption of low magnetic Reynolds number and involved numerical codes that utilized electric potential as the main electromagnetic variable. One limitation of this approach is that such codes cannot be applied to truly unsteady processes, for example, MHD flows of liquid-metal breeder/coolant during unsteady events in plasma, such as major plasma disruptions, edge-localized modes and vertical displacements, when changes in plasmas occur at millisecond timescales. Our newly developed code MOONS (Magnetohydrodynamic Object-Oriented Numerical Solver) uses the magnetic field as the main electromagnetic variable to relax the limitations of the low magnetic Reynolds number approximation for more realistic fusion reactor environments. The new code, written in Fortran, implements a 3D finite-difference method and is capable of simulating multi-material domains. The constrained transport method was implemented to evolve the magnetic field in time and assure that the magnetic field remains solenoidal within machine accuracy at every time step. Various verification tests have been performed including purely hydrodynamic flows and MHD flows at low and finite magnetic Reynolds numbers. Test results have demonstrated very good accuracy against known analytic solutions and other numerical data.

Pub.: 05 Apr '16, Pinned: 28 Jun '17